Dynamical brain model for use in data processing applications

ABSTRACT

A system and methods offering a dynamical model of cortical behavior is provided. In an illustrative implementation, the present invention offers a corticonic network comprising at least one parametrically coupled logistic map network (PCLMN)( 205 ). The PCLMN offers a non-linear iterative map of cortical modules (or netlets) that when executed exhibit substantial cortical behaviors. The PCLMN accepts dynamic and/or static spatio-temporal input ( 210 ) and determines a fixed point attractor in state-space for that input. The PCLM ( 205 ) operates such that if the same or similar dynamic and/or static spatio-temporal input is offered over several iterations, the PCLMN converges to the same fixed point attractor is provided rendering adaptive learning. Further, the present invention contemplates the memorization or association of inputs using the corticonic network in a configuration where the PCLMN cooperates with another cortical module model (e.g. another PCLMN, associative memory module, etc.)( 215 ).

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is the National Stage of International Application No.PCT/US02/05555, filed Feb. 25, 2002, which claims the benefit of U.S.Provisional Application No. 60/270,981, filed Feb. 23, 2001.

FIELD OF THE INVENTION

The present invention relates to the field of modeling brain activityfor use in data processing applications. More particularly, the presentinvention relates to providing a dynamical brain model of the cortex foruse in various data processing applications.

BACKGROUND OF THE INVENTION

Corticonics, echoing electronics, is the art of identifying anatomicalan physiological attributes of cortical organization to be abstractedand used in the modeling and simulation of the cortex. Generally, thecortex, in conjunction with the subcortical centers, is responsible forall higher-level brain functions such as cognition, thought, language,memory and learning, control of the complex motor function, and possiblythe more esoteric attributes of intention, awareness and consciousness.In fact, about 75% of all human brain tissue, defining the associationcortices is devoted to these functions. Thereby, understanding theworkings of the cortex can have profound scientific, technological, andclinical implications. Unfortunately, the intrinsic interest of thesehigher-level functions is equaled by the difficulties involved—bothtechnical and conceptual—in understanding their neurobiological basis.Nonetheless, progress to further this incomplete understanding is beingmade through studies of brain tissue that is damaged or has lesions,from in vivo imaging of the brain, and from electrode and patch-clampstudies in non-human primates. These studies aim at developing acomplementary computational approach to modeling and studying the cortexemploying the concepts and tools of nonlinear dynamics.

The non-linearity and organization of cortical tissue make the cortex ahigh-dimensional non-linear dynamical system. As such, it exhibits inits state-space not only static (fixed point) attractors but alsodynamic (periodic, quasi-periodic and chaotic) attractors depending onits location in parameter space. However, important questions remainunanswered about these brain functions and, specifically, about the roleof attractors in cortical cognitive processes. An assumption is that themost obvious role for attractors is to make it possible to operate on orutilize the activity trace caused by a stimulus after the stimulus hasdisappeared. Several important inquiries result from this assumption.Namely, 1) Is a particular attractor associated with the recognition ofa particular object or stimulus?; 2) Is the setting of cortical activityonto an attractor state synonymous with the recognition process?; and 3)Is such persistent activity needed for the formation of memory?

Current modeling practices fall short of providing answers to theseresulting inquiries. Neural networks are the predominate model used toexplain brain functions and how these brain functions could be mimickedin computing environments. Specifically, a neural network is aninformation processing paradigm that is inspired by the way biologicalnervous systems process information. The key element of this paradigm isthe novel structure of the information processing system. It isgenerally composed of a large number of highly interconnected processingelements (neurons) working in unison to solve specific problems. Neuralnetworks have an ability to derive meaning from complicated or imprecisedata. This ability can be used to extract patterns and detect trendsthat are too complex to be noticed by either humans or other computertechniques.

However, current brain computational models do not effectively predictthe behavior observed in the cortex. Stated differently, current modelsdo not effectively choose those features of cortical organization tomake salient in the model and eliminate and ignore those features ofcortical organization that do not provide any added benefit. The test ofthe model lies in how well it can produce, predict, and synthesizecortical functions. Current models, although effective in providing ageneral model for brain and/or nervous system functions do noteffectively and reliably model detailed cortical functions—functionsthat if properly modeled could provide substantial insight to how toprocess large volumes of data. Such insight may be applied to numerousdata intensive processing applications to improve processingefficiencies. With increased processing efficiencies computingtechnologies could be used to automate numerous manual tasks—manualtasks that we take for granted, such as voice recognition and synthesis,data searching, basic learning, etc.

From the foregoing it is appreciated that there exists a need forcomprehensive systems and methods offering a dynamical brain model, andspecifically the cortex, that may be applied to various data processingapplications. The present invention meets this pressing need in the art.

SUMMARY OF THE INVENTION

A system and methods to create a dynamical brain model for use in dataprocessing and synthesis applications is provided. In an illustrativeimplementation, the present invention offers a corticonic networkcomprising at least one parametrically coupled logistic map network(PCLMN). The PCLMN offers a non-linear iterative map of cortical modules(or netlets) that when executed exhibit substantial cortical behaviors.The PCLMN accepts dynamic and/or static spatio-temporal input anddetermines a specific attractor in state-space for that input. The PCLMNoperates such that if the same or similar dynamic and/or staticspatio-temporal input is offered over several iterations, the PCLMNconverges to the same attractor. As such the PCLMN engages in adaptivelearning. That is, based on a series of slightly varying inputs, thesame output is provided.

Further, the present invention contemplates the memorization orassociation of inputs using the corticonic network in a configurationwhere the PCLMN cooperates with another cortical model module (e.g.another PCLMN, associative memory module, etc.). In this context, thePCLMN provides an output. The output is then processed by thecooperating cortical model module to determine if the output is novel.If the output is novel, it is classified as such. However, if the outputhas been processed before by the cooperating cortical model module, theoutput is classifies as being “remembered” and may be stored as such.That is, for a repeating output of the PCLMN, the remaining modules ofthe cortical model operate to classify in real-time and without the aidof any memory elements if the output PCLMN data is novel or non-novel.Furthermore, in the implementation provided, the cooperating additionalcortical model module operates to associate a label to the attractoroutput of the exemplary PCLMN. This label for each attractor is thenstored in the additional cooperating cortical model module. Inoperation, this label is easily retrieved to identify one or moredynamic and/or static inputs offered to the cortical network.

Further, the present invention contemplates the use of a feedback loopoperating from the output of the additional cooperating cortical modelmodule to the input of the exemplary PCLMN. By having the feedback loopit is possible to design a specific and desired path in state space. Theability to design a specific and desired path in state space providesthe foundation for a model of how the cortex synthesis data (e.g. speechsynthesis). Further, the corticonic network can be configured to operatesuch that feedback loops are present between elements of a state-spacepath thereby modeling periodic cortical operational functions (e.g. howthe cortex controls walking, breathing, etc.).

Other features of the present invention are described below.

BRIEF DESCRIPTION OF THE DRAWINGS

The system and methods providing a dynamical brain model of the cortexare further described with reference to the accompanying drawings inwhich:

FIG. 1 is a block diagram of an exemplary schematized unfolded andflattened cortical patch in accordance with the present invention;

FIG. 2 is a system diagram of an exemplary corticonic network for use ina dynamical brain model in accordance with the present invention;

FIG. 2A is a system diagram of the exemplary conrticonic network havinga feedback loop to allow for state-space path design for us in adynamical brain model in accordance with the present invention;

FIG. 3 is a chart diagram of an exemplary state-space trajectory inaccordance with the present invention;

FIG. 3A is a chart diagram of an exemplary state space trajectorywherein periodic cortical operation functions and cortical abstractionare represented in accordance with the present invention;

FIG. 4 is a flow diagram of the processing performed by the exemplarydynamical cortical model system of the present invention when processinginputs to realize adaptive learning; and

FIG. 5 is a block diagram showing of the processing performed to applythe exemplary dynamical cortical model of the present invention when todata processing applications.

DETAILED DESCRIPTION OF ILLUSTRATED IMPLEMENTATION

Overview

Corticonic networks are biologically inspired and are naturally suitedfor handling dynamic input patterns. These networks incorporateabstractions of known attributes of cortical organization and function.The overwhelming complexity of cortical tissue on the microscopic levelof neuronal wiring and synaptic connections offer considerable obstaclesin developing a computationally efficient microscopic approach tomodeling the cortex and its functions. Despite notable progress in“reverse-engineering” the cortex on a sufficiently detailed level, manyof the obstacles in modeling the cortex still remain. Specifically, thelarge number of neurons per millimeter cube of cortical tissue (˜10⁵)and the dense connections between them (10³ to 10⁴ connections perneuron, resulting to approximately 3 km of axonal lengths per mm³)render the computational complexity of a detailed model of such as smallvolume of cortex as extensive if not exhausting. Moreover, thechallenges in trying to model the entire cortex or even a cortical patchwould be nearly impossible.

Simply, the challenge in modeling a complex system like the cortex is todecide which features of cortical organization to make salient in themodel and which features to eliminate or ignore. This challenge isfurther exacerbated as the model should have the ability to predictbehavior observed throughout the entire cortex. Ultimately, the test ofthe model lies in how well it can produce, predict, and synthesizecortical functions. With this simplification an inquiry results, namely,does the model exhibit the desired behavior because of thesimplification, or despite the simplification. Accordingly, a model thatdescribes the cortex too closely may result in an intractable model thatprovides little insight into desired cortical functions.

Current brain theory models attempt to model brain functions on a macroscope. The predominate model used is known as neural networks. Neuralnetworks are premised on a processing theory inspired by biologicalprocessing systems, such as the brain. The key element to neuralnetworks is the novel structure of the information processing systems.In the case of neural networks, the novel structure that is beingemulated is the brain. In the human brain, a typical neuron collectssignals from other through a host of fine structures called dendrites.The neuron sends out spikes of electrical activity through a long, thinstrand known as an axon, which splits into thousands of branches. At theend of each branch, a structure called a synapse converts the activityfrom the axon into electrical effects that inhibit or excite activityfrom the axon into electrical effects that inhibit or excite activity inthe connected neurons. When a neuron receives excitatory input that issufficiently large compared with its inhibitory input, it sends a spikeof electrical activity down its axon. Learning occurs by changing theeffectiveness of the synapses so that the influence of one neuron onanother changes. Neural networks are constructed premised on anunderstanding of the essential features of neurons and theirinterconnections. The networks may be modeled in a computing environment(e.g. software) to simulate this understanding. These models, however,are gross idealizations of real networks of neurons since the knowledgeof neurons and their interaction is incomplete.

Specifically, present day neural network and connectionist models of thecortex have not been effective in duplicating higher-level brainfunction and especially the ability of the. cortex/brain to processdynamic input patterns (e.g., the spatio-temporal signals furnished bysensory organs under the influence of a complex uncontrolled and dynamicenvironment or alternately due to deliberate dynamic exploration ofstationary environment or its reflexive exploration as by fast saccadiceye movement or touch). These shortcomings may be rooted in the models'use of simplistic transfer-function description of processing elementsand the use of the stimulus-response paradigm that both together orindependently do not accurately represent the way the cortex reacts tosensory information. The cortex is the seat of all higher-level brainfunction such as cognition, thought, language, memory and learning,control of complex motor functions and possibly the more esotericattributes of attention, awareness and consciousness. Accordingly, abetter understanding of cortical dynamics can have profound scientific,technological, clinical, and economic implications.

The present invention aims to ameliorate the shortcomings of currentlyused models by providing comprehensive systems and methods toeffectively model cortical functions such that the model is salient andmaintains necessary level of abstractions so as to better describecortical organizational and computational functions. The presentinvention is premised on a different viewpoint than the traditionallyaccepted and employed transfer-function and stimulus-response paradigm.This new viewpoint is that the cortex is a high-dimensional nonlineardynamical system that is continually active because of extensivefeedback and reentrant signaling. The effect of the extrinsic (sensory)input patterns, which are usually dynamic, is to alter the system'sstate-space picture leading to behavioral changes and to adaptation andlearning. Accordingly, the behavior of the cortex is viewed asdetermined by the conjugation of extrinsic stimulus with the internaldynamics of the system that serve to furnish the context within whichthe sensory input gets processed and interpreted.

In an illustrative implementation, the system of the present inventioncomprises at least one parametrically coupled logistic map network(PCLMN) that act to model the cortex as groups of tightly coupledneurons that form basic functional units known as netlets or corticalcolumns. The PCLMN allows for effective modeling of cortical functionsusing a difference equation that represent the neurons in the netlet orcolumns rather than having to solve for coupled systems of nonlineardifferential equations. As such, the present invention iscomputationally more effective and provides a basis for investigationsrelating to the spatio-temporal dynamics of large assemblies of PCLMs inreal time and, more particularly, to determine the consequences ofmodeling the cortex with networks of PLCMs.

The PCLM exhibits significant corticomorphic behavior. Such behaviorincludes: the handling of dynamic (i.e. spatio-temporal) input patterns,self-organization, and autonomous (unsupervised) learning from oneexposure (“one shot” learning) driven by mutual-information(MI—information theoretic measure of the flow of information betweenelements of a network), memory formation with negligible cross-talk,emergence of stimulus (input) or specific isolated clusters of activityreminiscent to hot spots of brain activity routinely pinpointed byfunctional magnetic resonance imaging (fMRI), automatic detection andreduction of redundancy in input patterns leading to sparse internalrepresentations that boost storage capacity, provision of huge number ofcoexisting attractors available for input patterns to draw upon,computing with diverse attractors possessing basins of attraction thatfurnish a mechanism for learning with generalization, and a role forsynchronicity, bifurcation, symmetry-breaking, and chaos in theoperation of the new class of networks.

In operation, the PCLMNs are arranged in various configurations andmaintain various configuration variables to provide a comprehensive anddynamical model of cortical organization and computational functions. Assuch, the present invention offers comprehensive system and methods toovercome the shortcomings of the art.

Illustrative Dynamical Brain Model

There are several salient features and principles of corticalorganization that shed light on the efforts of developing acomputationally efficient model and macroscopic theory of the cortex.One such organizational principle is the view of an unfolded andflattened cortex as a 2-D array of vertical units (vertically orientedmodules, columns, or netlets of neurons). As shown in FIG. 1, cortexpatch 100 comprises vertically oriented modules, columns, or netlets ofneurons 105. These netlets engage in short-range (intercortical)communications as indicated by arrows 110, and in long-rangecortico-cortical connections 115. It is understood that these netletsoperate to pass information between each other when processing datathrough axonal fibers 120. The nature and method of this operationprovides the basis for cortical organization and computationalfunctions.

As shown in FIG. 1, an illustrated second cortical organizationalprinciple suggests that the basic functional unit in the cortex is thecortical module (or netlet) and not the single neuron. The corticalmodule (or netlet) consists of a columnar organization of 10³-10⁴cortical neurons acting as a functional unit and that a netlet hasemergent functional behavior that can be mathematically modeled by aparametrically coupled (i.e. driven) logistic map (PCLM). Logistic mapsare further described by, Chaos and Nonlinear Dynamics, R. C., Hillborn,Oxford University Press, New York (1994), which is herein incorporatedby reference in its entirety. The PCLM may be considered a non-lineariterative map of the unit interval having extremely rich and complexbehaviors. It is also understood that cortical modules (netlets)interact via two types of connections, local connections, i.e. viaclose-range connections mediated by horizontal intercortical connections110, and via longer-range cortico-cortical connections 115 that connectmodules (columns) in different parts of the cortex or a cortical patch100 through axonal fibers (association fibers) 120.

Although there is little detailed information about how short and longrange cortical connections augment each other and contribute to thecortex's processing power, it is understood that the short-rangeintercortical connections between the modules form a network thatengages in a non-linear space-time filtering of dynamic sensory inputactivity relayed to it by the thalamus and the sensory cortices. Theaction of this network has been observed to self-organize under theinfluence of initial inputs so as to produce stimulus-specific sparsepatterns of activity for all subsequent inputs. Such sparse activitydrives other parts of the cortical columns assumed to form anothernetwork through the long-range cortico-cortical connections and toengage in associative learning and memory formation.

As seen in FIG. 1, the illustrated connections 110 and 115 can bedescribed as each column 105 being arbitrarily subdivided across thecortical layers into two interacting subunits. Each subunit comprises anetlet that may be modeled by a PCLM. One netlet pair (PCLMN) forms afirst network, PCLMN1, via the short-range intercortical connections110, while the other netlet pair (PCLMN) forms a second network, PCLMN2,via the longer-range cortico-cortical connections. In operation, the twonetworks interact to realize the storage and retrieval of globalactivity patterns. Based on this description, a corticonic model of thecortex is created. The network includes, as its basic ingredients, therole of both sort-range and long-range connections in memory formation,specific architecture or connectivity, nonlinear activity-dependentcoupling between processing elements, self-organization throughautonomous adaptation of coupling factors driven by mutual information(MI). The remaining ingredients of the model are the PCLMs as theprocessing elements in the network. These PCLMs mathematically model thecomplex emergent behavior of a cortical column or netlet, and thegradual transfer of control over the dynamics from extrinsic control tointrinsic control (i.e. by the input pattern, or by internal feedback togenerate persistent activity patterns constituting attractors thatcharacterize the input stimulus depending on the state of coupling inthe network).

Illustrative Corticonic Network

FIG. 2 shows an illustrative corticonic network 200. As shown in FIG. 2,two PCLMNs are connected in tandem. The first PCLMN1 205 has local (selfand nearest) neighbor connections that model the close-rangeintercortical connections. In operation, it engages in space-timefiltering of dynamic input patterns 210 that represent sensation relatedto dynamic input patterns relayed to the cortex by the thalamus and thesensory cortices. In the implementation provided, these input patterns210 may be regarded as dynamic feature vectors {right arrow over(X)}^(s)(n). The function of PCLMN1 205 is to reduce redundancy in theinput pattern {right arrow over (X)}^(s)(n) by producing for every inputpattern a persistent stimulus-specific sparse pattern for activitydesignated {right arrow over (X)}(n) which can be viewed as anattractor. This is accomplished by fine-tuning its initial couplingmatrix via an autonomous (unsupervised) adaptation algorithm driven bymutual information (MI) of the pair-wise activities (orbits) ofprocessing elements (PEs) in the network. This behavior constitutes aprocess of self-organization by MI and therefore by the flow ofinformation in the PCLM networks. As a result of its limited (self andnearest neighbor) coupling, PCLMN1 210 does not distinguish betweennovel and familiar inputs despite the adaptation of its initial couplingmatrix. This task is relegated to PCLMN2 215 that converts the input toa second persistent activity pattern (attractor) {right arrow over(Y)}(n) that characterizes {right arrow over (X)}(n). The adaptation ofthe elements of the coupling matrix of PCLMN2 215 is also driven bymutual information. The configuration of PCLMN2 215 (e.g. the equationsused to model PCLMN2) endow it with the cognitive ability ofdistinguishing a novel input {right arrow over (X)}(n) from a familiarone and the ability of autonomously learning the novel, but onlyproducing the appropriate response (attractor) for the familiar.

It is appreciated that although the exemplary corticonic network 200 isshown having a configuration of two PCLMNs in tandem that suchconfiguration is merely exemplary as the present invention contemplatesa corticonic network model having one or more PCLMNs, associative memorymodules, or other brain (cortical) modeling module cooperating variousconfigurations to achieve the inventive concepts described herein.

The processing elements, the PLCMs, within each PCLMN1 205 and PCLMN2215 interact via fixed connectivity patterns. The connectivity patternswithin both networks are random and so are the initial connectionstrengths. In doing so, the useful function of these networks is to alarge degree the result of self-organization via adaptation and learningand to a lesser degree due to any initial inbuilt structure. Thisenables two corticonic networks immersed in the same environment andtherefore subject to the same types of stimuli, to end-up acquiring thesame behavior through learning, even through their initial connectivitypatterns are not the same. The random connection patterns once set, toreflect the local and semi-global (wiring) of the cortex, remain fixed;only the strength of the connections, i.e. the coupling strengthsmatrix, is altered by MI driven adaptation. The coupling of the PCLMNsmay be represented as coupling matrices {right arrow over (C)}. Thecoupling between the networks may be considered to be one-to-one. Theinitial coupling factors matrix of PCLMN1 205 is local withself-coupling (diagonal elements) and nearest neighbor coupling set withthe probability Pr<1 (i.e. note every element in PLCMN1 205 is connectedto its nearest neighbors). In contrast, the coupling factors matrix ofPCLMN2 215 is set to be semi-global, sparse and void of self-coupling(i.e. no diagonal elements) and also void of short range connections.

The PCLMNs of FIG. 2 (i.e. PCLMN2 205 and PCLMN2 215) may be furtherdescribed by their one dimensional topologies to enable the display ofthe evolution of their state vectors {right arrow over (X)}(n) and{right arrow over (Y)}(n), respectively. Both networks employ nonlinearactivity dependent coupling functions between processing elements whichare more general than linear coupling. Nonlinear coupling contributes tothe self-organization of the network through competing forces of orderand disorder. In addition, in PCLMN1, control over the dynamics of thenetwork is transferred gradually from initially entire extrinsic controlby the applied stimulus 210 to eventually intrinsic control. Bothnetworks have double dynamics proceeding at different rates: fastdynamics controlling the evolution of the state vectors, i.e. the statesof the PEs (the PCLMs), and slower dynamics controlling the evolution ofthe coupling strengths between the PEs.

PLCMN1 205 is described by the following mathematical formulation.Specifically, the orbit of X_(i)(n) of the i^(th) PCLM or PE in PCLMN1205 may be expressed by,X _(i)(n+1)=μ_(i)(n)X _(i)(n)(1−X _(i)(n))i=0,1, . . . N−1 andn=0,1,2,  (1)Where X_(i)(n) is confined to the interval [0,1], and μ_(i)(n) to theinterval [0,4]. The initial state X_(i)(0) in equation 1 is selectedrandomly in [0,1] with uniform probability, while the parameter μ_(i)(n)is taken to be a function of the extrinsic stimulus (input) 210 X_(i)^(s)(n) and the intrinsic input (feedback) from other elements in thenetwork connecting to the i^(th) element in accordance to,

$\begin{matrix}{{\mu_{i}(n)} = {{{\mu_{i}^{s}(n)}{\mathbb{e}}^{{- \alpha}\; n}} + {\frac{1 - {\mathbb{e}}^{{- \alpha}\; n}}{N_{i}}{\sum\limits_{j \in {N_{i}}}{g_{i\; j}\left( {X_{j}(n)} \right)}}}}} & (2)\end{matrix}$where,μ_(i) ^(s)(n)=4(X _(i) ^(s)(n))^(C) i ^(s) and  (3)g _(ij)(X _(j)(n))=4(X _(j)(n))^(C) _(ij)  (4)are nonlinear activity dependent coupling functions, the first of whichrepresents the coupling of the i^(th) input X_(i) ^(s)(n) into thenetwork, and the second the coupling of the j^(th) element to thei^(th). C_(i) ^(S) and C_(ij) are positive real coupling factors thatcontrol the form of the activity dependent coupling function and furnishthe means for incorporating autonomous adaptation learning in thecorticonic net. The set |N_(i)| is the number of elements connecting tothe i^(th) element.

Taking a closer look at the right hand side of equation (2), the firstterm represents the effect of the external input X_(i) ^(s)(n) anddecays exponentially in time with rate constant α; the second termrepresents the effect of internal feedback from other elements which isseen to grow exponentially in time with rate constant α. In thisfashion, as the effect of the first term diminishes getting weaker intime, that of the second term becomes stronger effecting thereby thetransfer of control over the dynamics of PCLMN1 205 from extrinsic tointrinsic control. This handing-over of control over the dynamics ofextrisic to intrinsic is to avoid the network being permanently forcedby the input, giving thereby an opportunity for the interactions betweenits elements to exert their influence in determining the final state(convergent state) of the network. This, however, does not mean that thefinal state bears no relation to the resolved attractor {right arrowover (X)}*(n); to the contrary, the final state is stimulus specific.The first term in equation (2) is an exponentially decaying forcingfunction that acts in effect as a “soft” initial condition that guidesthe network to certain region of its state-space where the exponentiallyincreasing intrinsic dynamics, represented by the second term inequation (2), gradually take over leading the network to an attractor, apersistent stimulus-specific state characteristic of the particular{right arrow over (X)}^(s)(n). When these equations are simulated, it isobserved that the final state (attractor) reached by PCLMN1 205 isdependent of {right arrow over (X)}^(s)(n), its coupling factorsfunction matrices ({right arrow over (C)}^(s), {right arrow over (C)})and is independent of the initial state {right arrow over (X)}(0).

In operation, responding to a first stimulus, PCLMN1 205 having symmetrybreaking, initial local random connectivity, and coupling, generateschaotic excitation (activity) that represents the immense space ofpossible configurations (e.g. co-existing attractors) the network iscapable of maintaining. The number of possible states (coexistingattractors) is immense even for a modest size network. The descriptionof the state-space is observed to occur through a cascade ofbifurcations driven by mutual information, i.e. by the flow ofinformation between elements of a network. The resulting adaptation ofthe initial coupling strengths matrix constitutes self-organization ofPCLMN1 205 caused by the first applied stimulus. The application of asecond stimulus to the adapted PLCMN1 205 causes furtherself-organization but less vigorously than occurred with the firstapplied stimulus. The MI driven adaptation and self-organization becomeprogressively less vigorous with the application of further new stimuli(inputs) until a structured coupling factor matrix {right arrow over(C)} is reached where applied stimuli cause no adaptation but merelyselect directly one of the coexisting attractors.

Under simulation, PCLMN1 205 is observed to self-organize by adaptingits initial random coupling strengths matrix into a stable structurematrix that endows it with the very desirable attributes and properties.Namely, the ability to rapidly convert every distinct input stimulus,regardless of whether it is static or dynamic, into a distinct attractorthat is one of an immense number of coexisting fixed-point attractorsthe network can possess. Furthermore, it provides evidence thatattractors possess basins of attraction in stimulus space. Theconvergence of the adapted (self-organized) PCLMN1 205 to stimulusspecific attractors occurs very rapidly. Also, PLCMN1 205 maintains theability to detect and remove redundancy (regularity and form) in theapplied stimulus such to transmit or convert the input into the compactform of an attractor lending to the operation of creating memory orassociation.

As shown in FIG. 2, corticonic network comprises a second PCLMN2 215.PCLMN1 205 and PCLMN2 215 may be coupled to model memory and associationcortical functions. Specifically, PCLMN2 215 may be configured such thatit is able to accept the set of persistent output activities(attractors) {right arrow over (X)}(n), produced by PCLMN1 205 and mapthem into a new set of attractors in such a way that only a novel {rightarrow over (X)}(n), not seen by PCLMN2 215 before, would trigger itsadaptation to get “learned” and memorized as a characterizing attractor.This operation is performed such that when the identified attractors(i.e. identified by PCLMN2 215) are observed again they would be treatedas a familiar input that, merely elicits, or reconstructs thecharacterizing attractor without triggering adaptation. This memoryprocess occurs such that the adaptation by and learning of novel inputwould not interfere with earlier memories/attractors formed in PCLMN2215. In this manner, the simple tandem connection of PCLM1 105 andPCLMN2 15 in FIG. 2 forms corticonic network 200 processing he desirableattributes of PCLMN1 205 augmented by the cognitive ability of PCLMN2215 of differentiating between familiar and novel inputs by learning thenovel and producing the proper response for the familiar.

Akin to PCLMN1 PCLMN2 215 is mathematically modeled to be described bythe following equations (i.e. the evolution of state-vector {right arrowover (Y)}(n)),Y _(i)(n+1)=λ_(i)(n)Y _(i)(n)(1−Y _(i)(n))i=0,1,2, . . . N−1 andn=−,1,2,  (5)and

${\lambda_{i}(n)} = {4{\left( {X_{i}(n)} \right)^{C_{i}}\left\lbrack {{\mathbb{e}}^{{- \gamma}\; n} + \left( {1 - {{\mathbb{e}}^{{- \gamma}\; n}\min\left\{ {{\sum\limits_{j \in {N_{i}}}\left( {Y_{j}(n)} \right)^{C_{i\; j}}},1} \right\}}} \right\rbrack} \right.}}$where γ is a positive real constant, N_(i) is the number of maps (i.e.PCLMs or processing elements (PE)) connecting to the i^(th) map, |N_(i)|is the set of indices of all maps connection to the i^(th) map, C_(i)^(S) is a fixed positive real constant determining how different valuesof the stimulus X_(i)(n) (i.e. the output of PCLMN1205 influence thei^(th) map or PE. C_(ij) is the coupling factor between the j^(th) andi^(th) maps (PEs) that get adapted from initial value C_(ij)(0) by themutual information (MI) between the j^(th) and I^(th) orbits as inPCLMN1 205.

Using these equations, corticonic network 200 may be simulated in anexemplary computing application to show how PCLMN1 205 realizes adaptiveresponse to dynamic and/or static inputs and correspondingly how thetandem PCLMN1 205 and PCLMN2 215 combination offers memory and/orassociation operations for one or more inputs. These importantoperations offer a simple, workable, and robust model of desiredcortical organization and computational functions. The reliability ofthis model is verified through comparisons to biological corticalfunctions as observed through functional Magnetic Resonance Imaging(fMRI) studies.

FIG. 2A shows an alternate implementation of corticonic network 200′. Asshown, corticonic network comprises PCLMN1 205′ accepting dynamic and/orstatic inputs from input source 210. PLCMN1 205′ is tandemly coupled toadditional cortical model module 215′ (e.g. PCLMN, associative memory,etc.) such that the output attractors of PCLMN1 205′ act as input toadditional cortical model module 215′. Further, the output of additionalcortical model module 215′ is fed back through feedback loop 225′ to actas input to PCLMN1 205′.

In operation, corticonic network 200′ of FIG. 2A allows for the designof a desired path in state-space (as illustrated in FIGS. 3 and 3A).Stated differently, corticonic network 200′ can be formed by PCLMN1 205′coupled in tandem with a hetero-associative memory 215′ to model thethalamo-cortical complex of the brain. Because of the enormous number ofcoexisting input-specific attractors held in PCLMN1 205, ebery inputpattern (e.g. feature vector μ_(i) ^(s)(n)) is guaranteed to produce afixed-point attractor as output. The role of the hetero-associativememory 215′ is to tag the attractors of the PCLMN, produced by theindividual inputs, with labels ({right arrow over (L)} 220′) so as toidentify the inputs. With feedback 225′ and systematic pairing ofattractor-label associations stored in thee associative network(memory), it is possible to form a predetermined sequence ofassociations (patterns) in response to an input. This is equivalent toforming a trajectory (as shown in FIGS. 3 and 3A) in the state-space ofcorticonic network 200′.

FIGS. 3 and 3A show exemplary desired trajectories existing instate-space. As shown in FIG. 3, state-space trajectory 300 comprises aseries of fixed point attractors and labels. These fixedpoint-attractors and labels have known positions in state-space.Accordingly, it is possible to generate a desired trajectory instate-space by providing an input that will produce the an attractorthat represents the first point of a desired trajectory in the statespace (e.g. {right arrow over (X)}_(A1)). This attractor is providedwith a label (e.g. {right arrow over (L)}_(A1)) having its own positionin state space and representing the second point along the desiredtrajectory. The label is the feedback into the corticonic network toproduce a second attractor (e.g. {right arrow over (X)}_(A2)) thatrepresents a third point along the desired trajectory. The secondattractor is labeled and then the label is fed back. This processcontinues until the final point of the desired trajectory (e.g. {rightarrow over (C)}) is reached.

Specifically, state-space trajectory 300 is generated as input {rightarrow over (X)}^(s) _(A)(n) is processed by corticonic network 200′according to the above-described operation to produce the fixed-pointattractor {right arrow over (X)}_(A1) which in turn is then provided thelabel {right arrow over (L)}_(A1). Label {right arrow over (L)}_(A1)then acts as input to corticonic network 200′ that processes {rightarrow over (L)}_(A1) to produce a second fixed point attractor {rightarrow over (X)}_(A2) The second fixed point attractor is then providedthe label {right arrow over (L)}_(A2) which in turn is fed back to thenetwork to produce a third fixed-point attractor {right arrow over(X)}_(A3). Similarly, fixed point attractor {right arrow over (X)}_(A3)is provided with a label, {right arrow over (L)}_(A3) that is fed backinto corticonic network 200′ to produce fixed-point attractor {rightarrow over (X)}_(A4). Fixed point attractor {right arrow over (X)}_(A4)is then labeled as the final point {right arrow over (C)} along desiredstate-space trajectory 300.

In providing the ability to design a trajectory in state-space, thepresent invention allows for predictive data synthesis based on singleinput. This aspect of the cortical model of the present invention may beincorporated in data processing applications to synthesize predictivedata, such as speech. That is, spoken words can be modeled temporalvectors having certain trajectories in state-space of N dimensions. Acomputing application having incorporated the model of the presentinvention would be able to synthesize spoken words based on a singleinput.

FIG. 3A shows additional capabilities of the present invention asrelating to designing and executing trajectories in state-space. Asshown, state-space trajectory 300 of comprises a number of fixed pointattractors and labels. State-space trajectory 310 is similar tostate-space trajectory 300 of FIG. 3 but as seen has various additions(as indicated by dotted lines). Similar to the process described ingenerating state-space trajectory 300 of FIG. 3, state-space trajectory310 is generated by providing a first input {right arrow over (X)}^(s)_(A)(n) that produces a first attractor {right arrow over (X)}_(A1) andfirst label {right arrow over (X)}_(A1). Label {right arrow over(L)}_(A1) is fed back into corticonic network 200′ (of FIG. 2A) toproduce second attractor {right arrow over (X)}_(A2) having a secondlabel {right arrow over (L)}_(A2). The feed back process is repeateduntil the final state-space trajectory point {right arrow over (C)} isreached. Unlike, state-space trajectory 300 that accommodates a singleinput, state-space trajectory 310 is shown to accommodate several inputs{right arrow over (X)}^(s) _(A)(n), {right arrow over (X)}_(B)(n),{right arrow over (X)}_(C)(n), and {right arrow over (X)}_(D)(n).Further, {right arrow over (X)}_(B)(n), {right arrow over (X)}_(C)(n),and {right arrow over (X)}_(D)(n) are different than {right arrow over(X)}^(s) _(A)(n) in that the labels of the attractors that are producedas a result of these inputs are labels of points found along thetrajectory of state-space trajectory 300 as described by attractor-labelrelationship diagrams 310 a, 310 b, and 310 _(c) respectively.Specifically, as shown in relationship attractor-label 310 a input{right arrow over (X)}^(s) _(B)(n) produces attractor {right arrow over(X)}*_(B1) that in turn is assigned with label {right arrow over(L)}_(B1). However, as shown, {right arrow over (L)}_(B1) is not aunique label, but rather is the same label as {right arrow over(L)}_(A1) of state-space trajectory 300. As a result, and as seen onstate-space trajectory 310 in FIG. 3A, the state-space trajectory forinput {right arrow over (X)}^(s) _(B)(n) intersect that of state-spacetrajectory 300. The same holds true for inputs {right arrow over(X)}^(s) _(C)(n) and {right arrow over (X)}^(s) _(D)(n). That is, theresulting state-space trajectories for inputs {right arrow over (X)}^(s)_(C)(n) and {right arrow over (X)}^(s) _(D)(n) intersect the state-spacetrajectory 300 at different points along state-space trajectory. Thisresults as the label {right arrow over (L)}_(C1) assigned to resultingattractor {right arrow over (X)}*_(C1) is the same as label {right arrowover (X)}_(A2) as shown in attractor-label relationship diagram 310 b.Similarly, label {right arrow over (L)}_(D1) assigned to resultingattractor {right arrow over (X*)}_(D1) is the same label as label {rightarrow over (L)}_(A3) as shown in attractor-label relationship diagram310 c. Further attractor relationship diagram 310 c shows that {rightarrow over (L)}_(D1) has the same value as the original input {rightarrow over (X)}_(D)(n).

State-space trajectory 310 describes two features of corticalorganization and computation that the present invention has modeled.First, dissimilar instantiations of the concept {right arrow over (C)}of an object are provided. For example, if the four inputs {right arrowover (X)}^(s) _(A)(n), {right arrow over (X)}^(s) _(B)(n), {right arrowover (X)}^(s) _(C)(n), {right arrow over (X)}^(s) _(D)(n) are featurevectors describing the concept of a chair the present invention iscapable of designing a state-space trajectory such that the “chair”objects (i.e. feature vectors) are abstracted (converge) to a concept{right arrow over (C)} (state-space position) of a chair. The cortexoperates such that it can identify and store concepts for a range ofobjects that have features relating to the concept. In the example of achair, the cortex can identify a number of various objects based on theconcept chair, i.e. a construct to place items or to sit on. Thisconcept may encompass a number of features such as legs, a back, a seat,a horizontal surface, etc. The present invention achieves theabstraction of a concept by allowing for the design of specificstate-space trajectories that can accommodate multiple inputs andconverge these inputs through the assignment of similar labels to aspecific state-space position.

The second cortical feature highlighted by state-space trajectory 310 isthe realization of periodic functions. As shown in encircled region 310c′ the present invention allows for the creation and implementation of afeedback loop among points along the state-space trajectory itself.Encircled region 310 c′ goes further to describe the attractor-labelrelationship of attractor {right arrow over (X)}*_(D1) with input {rightarrow over (X)}^(s) _(D)(n) and labels {right arrow over (L)}_(D1) and{right arrow over (L)}_(A3). As seen a feedback loop is generatedbetween label {right arrow over (L)}_(A3) and {right arrow over(L)}_(D1). This loop represents the control of periodic function by thecortex. For example, walling is periodic function controlled by thecortex. It requires the movement of the first leg which is modeled byinput {right arrow over (X)}^(s) _(D)(n) that creates attractor {rightarrow over (X)}*_(D1) having label {right arrow over (L)}_(A3). Oncethat first leg is moved, the second leg requires moving. Accordingly,input {right arrow over (X)}^(s) _(D)(n) is required. This is achievedby equating label {right arrow over (L)}_(A3) with input {right arrowover (X)}^(s) _(D)(n). The result is a periodic movement of command-moveleg, step, move leg, step, etc. Once again the present inventionprovides a basis to model advanced cortical functions that existingcortical models are either incapable of modeling, or alternatively, areextremely inefficient in modeling.

FIG. 4 shows the processing performed to create a dynamical brain modelin accordance with the present invention. As shown, processing begins atblock 400 and proceeds to block 410 where a check is performed todetermine if a dynamic and/or static input has been provided. If aninput has not been provided, processing reverts to block 400 andproceeds there from. However, if at block 410 an input has beendetected, processing proceeds to block 420 where the input is processedby the PCLMN to establish a basin of attractors (or a single attractor)in state-space. A check is then performed at block 430 to determine ifthe input is novel. If the input is novel, processing proceeds to block450 and proceeds there from. However, if the input is deemed not to benovel at block 430, processing proceeds to block 440 where the PCLMNundertakes adaptation of the input. From there processing proceeds toblock 450 where a check is performed to see if the input is to bememorized or associated. If it is not, processing terminates at block470. However, if the input is deemed to be memorized or associated,processing proceeds to block 460 where is it processed by a secondcortical module (e.g. PCLMN, associative memory, etc.) wherememorization or association occurs. Processing then terminates at block470.

FIG. 5 shows the processing performed to apply the dynamical brain modelof the present invention to data processing applications resulting inapplications that process data in accordance to modeled corticalfunctions that improves processing efficiencies. As shown, processingbegins at block 500 and proceeds to block 510 where a processingdeficiency is identified. From there, processing proceeds to block 520where the corticonic network (using the inventive concepts describedherein) is designed to meet the needs of the identified problem. Atblock 530, the cortical network is configured with parameters to addressthe identified problem. From there processing proceeds to block 540where the corticonic network is built via exemplary computing softwareand hardware to execute processing to overcome the identified processingproblems. At block 550 the results of the corticonic network areverified. From there processing terminates at block 560.

Exemplary Data Processing Application Using Dynamical Brain Model

The dynamical brain model of the present invention may be applied tonumerous data processing application to improve efficiencies and providemore relevant results. It is appreciated that the data processingapplication described herein is exemplary as the inventive conceptsdescribed herein may be applied to various data processing applicationsincluding but not limited to database processing and managementapplications, sonar application, radar applications, voice recognitionand/or synthesis applications, etc.

The corticonic network of the present invention may be employed in anobject recognition concept inspired by the sounding and recognitionsystem of certain echo-locating mammals (e.g. the dolphin). It is wellknown that the dolphin uses sound not only to navigate and explore itsenvironment, but also to achieve and uncanny ability to recognizeobjects in its environment. It has also been observed in controlledexperiments that slight changes occur in the emission, the click,waveform used by the dolphin while it is engaging in a recognition taskand that the click waveform stops changing, i.e. converges, oncerecognition seems to have been achieved. It is as if the dolphin ischanging its emissions to discern the object better. Such operation ispuzzling since it remains a question how the dolphin succeeds to acquiremore information about a scattering object by means of click waveformsthat appear to change very little from click to click. This scenariosuggests that the dolphin is utilizing an iterative sounding andrecognition “loop” that involves not only the object, but also its soundgeneration and sensing system and its auditory, motor, and othercortices. The corticonic network of the present invention may beemployed to model the cortex part of this echoing loop to helpunderstand or explain the dolphin's remarkable recognition abilities.With this model and its ensuing results, new designs of new generationof intelligent sonar and radar capable of automated object recognitioncan be realized.

Further, the present invention does not merely offer insight that helpsto explain and predict cortical function and behavior, rather it alsoprovides new tools for use in applications involving the recognition andgeneration of spatio-temporal signals. These applications may share thecommonality that they are required to process the output of a filterbank that analyzes a waveform. A major obstacle yet not hurdled is howto form a representation of the output of the filter back that isinvariant with time-warping (a form of non-uniform scaling of the inputwaveform in time). In the context of the corticonic networks offered bythe present invention, this obstacle may be simply defined such that thenormalized version of the output of the filter bank is {right arrow over(X)}^(s)(n), the input to corticonic network 200. The corticonic network200 can produce attractors that are invariant with slight timedistortions of spatio-temporal input {right arrow over (X)}^(s) (n) tothe network. As such, the corticonic network may be employed to classifydynamic and/or static events as they unfold by means of sequences ofattractors that may be subsequently identified because of theirpersistence and invariance with time warping.

CONCLUSION

In sum, the present invention provides system and methods that offer adynamical brain model—a model that may be applied to various dataprocessing applications. It is understood, however, that the inventionis susceptible to various modifications and alternative constructions.There is no intention to limit the invention to the specificconstructions described herein. On the contrary, the invention isintended to cover all modifications, alternative constructions andequivalents falling within the scope and spirit of the invention.

It should also be noted that the present invention may be implemented ina variety of computer enviromnents (including both non-wireless andwireless computer environments), partial computing environments, andreal world environments. The various techniques described herein may beimplemented in hardware or software, or a combination of both.Preferably, the techniques are implemented in computer programsexecuting on programmable computers that each include a processor, astorage medium readable by the processor (including volatile andnon-volatile memory and/or storage elements), at least one input device,and at least one output device. Program code is applied to data enteredusing the input device to perform the functions described above and togenerate output information. The output information is applied to one ormore output devices. Each program is preferably implemented in a highlevel procedural or object oriented programming language to communicatewith a computer system. However, the programs can be implemented inassembly or machine language, if desired. In any case, the language maybe a compiled or interpreted language. Each such computer program ispreferably stored on a storage medium or device (e.g., ROM or magneticdisk) that is readable by a general or special purpose programmablecomputer for configuring and operating the computer when the storagemedium or device is read by the computer to perform the proceduresdescribed above. The system may also be considered to be implemented asa computer-readable storage medium, configured with a computer program,where the storage medium so configured causes a computer to operate in aspecific and predefined manner.

Although an exemplary implementation of the invention has been describedin detail above, those skilled in the art will readily appreciate thatmany additional modifications are possible in the exemplary embodimentswithout materially departing from the novel teachings and advantages ofthe invention. Accordingly, these and all such modifications areintended to be included within the scope of this invention. Theinvention may be better defined by the following exemplary claims.

1. A method to simulate cortical processing for use in processing data,comprising: segmenting a cortex into cortical columns, said corticalcolumns communicating with each other via short-range and longer-rangecommunications paths; generating at least one parametrically coupledlogistic map network (PCLMN) to model these communication paths, saidPCLMN comprising one or more parametrically coupled logistic maps; usinga difference equation in the PCLMN that represents neurons in thecortical columns in the modeling of the cortex; and configuring thePCLMN to perform acts comprising any of (a) handling dynamic and/orstatic input patterns, (b) handling large numbers of sensory stimuli,and (c) providing a solution to a plasticity-stability problem to memoryformation.
 2. A method to simulate cortical processing for use inprocessing data, comprising: segmenting a cortex into cortical columns,said cortical columns communicating with each other via short-range andlonger-range communications paths; generating at least oneparametrically coupled logistic map network (PCLMN) to model thesecommunication paths, said PCLMN comprising one or more parametricallycoupled logistic maps; using a difference equation in the PCLMN thatrepresents neurons in the cortical columns in the modeling of thecortex; providing at least one dynamic and/or static input to said atleast one PCLMN; and processing said at least one dynamic and/or staticinput by said PCLMN to determine a fixed-point attractor for said atleast one dynamic and/or static input in state-space.
 3. The method asrecited in claim 2, further comprising: offering said at least saidattractor by said PCLMN for similar or same said at least one dynamicand/or static input, said PCLMN engaging in adaptive learning to offersaid attractor.
 4. The method as recited in claim 3, further comprising:providing at least one additional cortical model module to cooperatewith said at least one PCLMN to perform memorization and/or associationoperations, said at least one additional cortical module comprising anyof a PCLMN and associative memory.
 5. The method as recited in claim 4,further comprising: providing a feedback loop to allow for the designand implementation of desired state-space trajectories, said feedbackloop originating from the output of said at least one additionalcortical model module and terminating at the input of said at least onePCLMN.
 6. The method as recited in claim 5 further comprising: labelingsaid determined attractor by said at least one additional cortical modelmodule for association and storage.
 7. The method as recited in claim 3,wherein said at least dynamic and/or static inputs comprise dynamicand/or static spatio-temporal stimuli.
 8. The method as recited in claim7, wherein said dynamic and/or static spatio-temporal stimuli originatefrom at least one filter, said filter comprising any of an electronicfilter, a partially-electronic filter, and a biological filter.
 9. Acomputer readable storage medium having computer readable instructionsto perform the steps recited in claim
 1. 10. A system to model corticalprocessing for use in processing data, comprising: a memory; at leastone parametrically coupled logistic map network (PCLMN) stored in thememory, said PCLMN providing a dynamic and/or static non-linearrepresentation of cortical connections as observed in a biologicalcortex using a difference equation that represents neurons in corticalcolumns, wherein said at least one PCLMN accepts at least one dynamicand/or static input and processes said dynamic and/or static input toidentify a fixed-point attractor for said at least one dynamic and/orstatic input in state space, wherein said at least one PCLMN operates toadapt providing the same output to similar or same inputs therebyengaging in learning; and wherein said at least one dynamic and/orstatic input comprises at least one spatio-temporal stimulus.
 11. Asystem to model cortical processing for use in processing data,comprising: a memory; at least one parametrically coupled logistic mapnetwork (PCLMN) stored in the memory, said PCLMN providing a dynamicand/or static non-linear representation of cortical connections asobserved in a biological cortex using a difference equation thatrepresents neurons in cortical columns, wherein said at least one PCLMNaccepts at least one dynamic and/or static input and processes saiddynamic and/or static input to identify a fixed-point attractor for saidat least one dynamic and/or static input in state space, wherein said atleast one PCLMN operates to adapt providing the same output to similaror same inputs thereby engaging in learning; and wherein said adaptationof said at least one PCLMN occurs through few iterations of inputs. 12.A system to model cortical processing for use in processing data,comprising: a memory; at least one parametrically coupled logistic mapnetwork (PCLMN) stored in the memory, said PCLMN providing a dynamicand/or static non-linear representation of cortical connections asobserved in a biological cortex using a difference equation thatrepresents neurons in cortical columns, wherein said at least one PCLMNaccepts at least one dynamic and/or static input and processes saiddynamic and/or static input to identify a fixed-point attractor for saidat least one dynamic and/or static input in state space, wherein said atleast one PCLMN operates to adapt providing the same output to similaror same inputs thereby engaging in learning; and at least one additionalcortical model module, said at least one additional cortical modelmodule accepting the output of said at least one PCLMN as input and iscapable of classifying in real time said output of said at least onePCLMN as being novel simulating memorization and/or association corticalfunctions.
 13. The system as recited in claim 12, wherein said at leastone additional cortical model module comprises any of a PCLMN andassociative memory.
 14. The system as recited in claim 13, wherein saidat least one PCLMN and said at least one additional cortical modelmodule are tandemly coupled.
 15. The system as recited in claim 14,wherein said at least one PCLMN and said at least one additionalcortical model operate synchronously.
 16. The system as recited in claim14 further comprising: a feedback loop originating from the output ofsaid at least one additional cortical model module and terminating atthe input of said at least one PCLMN, wherein said feed back loopallowing for the design and implementation of desired state-spacetrajectories.
 17. A method to model the cortex and use said model inorder to process input data, comprising: providing a corticonic network,said corticonic network comprising at least one parametrically coupledlogistic map network (PCLMN) operating on at least one dynamic and/orstatic input, said at least one dynamic and/or static input comprisingspatio-temporal stimulus and said PCLMN modeling cortical functionsusing a difference equation; processing said at least one dynamic and/orstatic input using said corticonic network; providing a fixed pointattractor in state space for said at least one dynamic and/or staticinput; and performing memorization and/or association on said outputs ofsaid corticonic network, said corticonic network engaging inmemorization through the use of at least one additional PCLMN tandemlycoupled to said at least one PCLMN and operating to classify noveloutput data from said at least one PCLMN in order to process the inputdata.
 18. A system modeling the cortex for use in processing datacomprising: a memory; a corticonic network, wherein said corticonicnetwork comprises a first parametrically coupled logistic map network(PCLMN) stored in said memory, said first PCLMN accepting dynamic and/orstatic inputs and determining a fixed point attractor in state-space todescribe at least one dynamic and/or static input, said first PCLMNmodels close-range intercortical connections by space-time filtering ofthe inputs in order to reduce redundancies in patterns of the inputsusing an autonomous adaptation algorithm, and wherein said corticonicnetwork comprises a second PCLMN, said second PCLMN tandemly coupled tosaid first PCLMN to accept the output of said first PCLMN as input andoperates to identify non-novel output of said first PCLMN, saididentification of non-novel output representative of memorization and/orassociation cortical functions, and wherein a feedback ioop operatesbetween the output of said second PCLMN and the input of said firstPCLMN.
 19. The system as recited in claim 18, wherein said corticonicnetwork comprises a computing environment.
 20. The method as recited inclaim 18, wherein said second PCLMN exhibits associative memoryattributes to label and associate attractors resulting from said firstPCLMN.
 21. A method of applying a dynamical brain model for processingdata comprising: identifying a data processing problem; modeling thedata processing problem in a corticonic network; configuring saidcorticonic network to the parameters of said data processing problem;executing said corticonic network using a computer, the corticonicnetwork modeled by a parametrically coupled logistic map (PCLM) thatmodels cortical functions using a difference equation; using thecorticonic network for processing the data and providing a processedoutput; obtaining results from said execution of said corticonicnetwork; and verifying said results of said execution of said corticonicnetwork by comparing said results of the processed output with acomparable real-world model.
 22. A computer readable storage mediumcomprising computer readable instructions to perform the steps recitedin claim 21 in order to process the input data.
 23. The method asrecited in claim 17, further comprising performing self-organization,wherein the self-organization comprises undertaking driven adaptationsuch that inputs to the corticonic network are rapidly classified usinginput-specific attractors.
 24. The method as recited in claim 17,further comprising employing chaos principles to perform the drivenadaptation.
 25. The method as recited in claim 17, further comprisingdistinguishing between structured and random input patterns.
 26. Themethod as recited in claim 17, further comprising ascertainingcoexisting attractors that are uniquely accessed by the inputs.
 27. Themethod as recited in claim 26, further comprising employing anassociative memory network to label the attractors, wherein theassociative memory network comprises a bank of -D optical holographicassociative memories.
 28. The method as recited in claim 17, furthercomprising labeling inputs with time specific attractors, wherein theattractor is exists for a set period of time.
 29. The method as recitedin claim 17, further comprising performing symmetry breaking, whereinthe symmetry breaking is realized by randomly selecting a fraction ofthe processing elements and isolating the elements from their neighbors.30. The method as recited in claim 29, further comprising partitioningthe corticonic network into sub-networks of unequal size that areisolated from each other.
 31. The method as recited in claim 17, furthercomprising inputting invariant feature-vector(s) of an object to thecorticonic network.
 32. The system as recited in claim 18, furthercomprising including a feedback from a labeling associated memory to thefirst PCLMN such that a cortical module is produces which is capable ofproducing discrete-time trajectories in the state-space of the corticalmodule.
 33. The system as recited in claim 32, wherein the trajectoriescan be fashioned to provide the cortical module withcategorical-perception and perceptual inference.
 34. The method asrecited in claim 21, further comprising processing spatio-temporal andstatic input patterns.